1891.] of the Excursions of the Capillary Electrometer, fyc. 173 



spending- to equal time-intervals are in arithmetical progression, and 

 the sub-tangent to the curve is of constant length. It was also 

 shown in the preliminary note that the tangent to a point on the 

 curve produced by an irregular change of electromotive force coin- 

 cides in direction with that of the normal curve produced by the 

 difference of potential existing at that instant between the terminals 

 of the electrometer, and on this was based a method of determining 

 the amount of that difference. 



Further Investigation of the Formula y = ae~ ct . 



Calibration Error. The greater the range of the excursion for a 

 given small difference of potential, the slower is the action of the 

 instrument. Hence, in the majority of capillaries, the rate of move- 

 ment decreases as the meniscus approaches the tip of the capillary. 



Change of Resistance. The shorter the length of dilute acid, the 

 smaller is the resistance, and the quicker is the motion; hence, in all 

 instruments there is a tendency to increased rapidity as the meniscus 

 approaches the tip of the capillary. The equivalent internal resist- 

 ance of an electrometer may be written 



where I = the length of the capillary beyond the meniscus at any 

 'moment, and L = a constant many times larger than Z, and repre- 

 senting the sum total of the mechanical and the remaining electrical 

 resistances. The effect of the change of resistance is so much smaller 

 that it may be completely masked and neutralised by the calibration 

 error, which has an opposite effect. 



Change in the Mode of Photographing the Excursions. 



In order to bring out the details of the electrical phenomena of 

 muscle, it was necessary to make the plates move faster than was 

 possible with the apparatus hitherto employed. To do this they were 

 attached to a kind of balanced pendulum and caused to describe an 

 arc of a circle. With this arrangement the normal excursion is best 

 expressed in polar coordinates. Time being recorded on a circular 

 arc, t becomes 0. Instead of the rectilinear asymptote there is an 

 asymptotic circle of radius = R. The expression for the radius vector 

 is r = R + 2/, the equation connecting y and 6 being y = ae~ c6 . With 

 such a curve the method of analysis first put forward is no longer 

 applicable. In place of it however there is a still simpler one. The 

 equation to the polar sub-normal, rcoiifs = drld6, is in this case 

 independent of R, being simply cy. In other words, the polar sub- 

 normal to a point on the curve is a constant multiple of its distance 



